4.12.36 $(1-x^{3}y(x))y^{\prime }(x)=x^{2}y(x{)}^2$

ODE
$$(1-x^{3}y(x))y^{\prime }(x)=x^{2}y(x{)}^2$$ ODE Classification

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 14.689 (sec), leaf count = 326

$$\{\{y(x)\to \frac{\sqrt[3]{12c_1{x}^6+2\sqrt{6}\sqrt{c_1{x}^6(6c_1{x}^6+1)}+1}+\frac{1}{\sqrt[3]{12c_1{x}^6+2\sqrt{6}\sqrt{c_1{x}^6(6c_1{x}^6+1)}+1}}+1}{2x^3}\},\{y(x)\to \frac{2i(\sqrt{3}+i)\sqrt[3]{12c_1{x}^6+2\sqrt{6}\sqrt{c_1{x}^6(6c_1{x}^6+1)}+1}-\frac{2(1+i\sqrt{3})}{\sqrt[3]{12c_1{x}^6+2\sqrt{6}\sqrt{c_1{x}^6(6c_1{x}^6+1)}+1}}+4}{8x^3}\},\{y(x)\to \frac{-2(1+i\sqrt{3})\sqrt[3]{12c_1{x}^6+2\sqrt{6}\sqrt{c_1{x}^6(6c_1{x}^6+1)}+1}+\frac{2i(\sqrt{3}+i)}{\sqrt[3]{12c_1{x}^6+2\sqrt{6}\sqrt{c_1{x}^6(6c_1{x}^6+1)}+1}}+4}{8x^3}\}\}$$

Maple ✓
cpu = 0.019 (sec), leaf count = 30

$$\{\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}-\frac{\ln (2x^{3}y\left(x\right)-3)}{6}-\frac{\ln \left(x^{3}y\left(x\right)\right)}{3}=0\}$$ Mathematica raw input

DSolve[(1 - x^3*y[x])*y'[x] == x^2*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> (1 + (1 + 12*x^6*C[1] + 2*Sqrt[6]*Sqrt[x^6*C[1]*(1 + 6*x^6*C[1])])^(-1
/3) + (1 + 12*x^6*C[1] + 2*Sqrt[6]*Sqrt[x^6*C[1]*(1 + 6*x^6*C[1])])^(1/3))/(2*x^
3)}, {y[x] -> (4 - (2*(1 + I*Sqrt[3]))/(1 + 12*x^6*C[1] + 2*Sqrt[6]*Sqrt[x^6*C[1
]*(1 + 6*x^6*C[1])])^(1/3) + (2*I)*(I + Sqrt[3])*(1 + 12*x^6*C[1] + 2*Sqrt[6]*Sq
rt[x^6*C[1]*(1 + 6*x^6*C[1])])^(1/3))/(8*x^3)}, {y[x] -> (4 + ((2*I)*(I + Sqrt[3
]))/(1 + 12*x^6*C[1] + 2*Sqrt[6]*Sqrt[x^6*C[1]*(1 + 6*x^6*C[1])])^(1/3) - 2*(1 +
 I*Sqrt[3])*(1 + 12*x^6*C[1] + 2*Sqrt[6]*Sqrt[x^6*C[1]*(1 + 6*x^6*C[1])])^(1/3))
/(8*x^3)}}

Maple raw input

dsolve((1-x^3*y(x))*diff(y(x),x) = x^2*y(x)^2, y(x),'implicit')

Maple raw output

ln(x)-_C1-1/6*ln(2*x^3*y(x)-3)-1/3*ln(x^3*y(x)) = 0